Related papers: Path Decomposition of Spectrally Negative Levy Pro…
We study spectral-theoretic properties of non-self-adjoint operators arising in the study of one-dimensional L\'evy processes with completely monotone jumps with a one-sided barrier. With no further assumptions, we provide an integral…
In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents.…
Gallai's path decomposition conjecture states that for a connected graph $G$ on $n$ vertices, there exists a path decomposition of size $\lceil \frac{n}{2} \rceil$. The Levi graph of order one, denoted by $L_{1}(m,k)$, is a bipartite graph…
In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master L\'evy measure and the associated L\'evy-It\^o…
In this article we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we set out to define a proper distance measure…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
The framework of the Perturbed Static Path Approximation (PSPA) is used to calculate the partition function of a finite Fermi system from a Hamiltonian with a separable two body interaction. Therein, the collective degree of freedom is…
This paper concerns optimal stopping problems driven by the running maximum of a spectrally negative L\'{e}vy process $X$. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping problem [Avram, Kyprianou…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely…
Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
Material decomposition in X-ray imaging uses the energy-dependence of attenuation to virtually decompose an object into specific constituent materials. X-ray phase contrast imaging is a developing technique that can enhance image contrast…
Let $\tau(x)$ be the first time the reflected process $Y$ of a Levy processes $X$ crosses x>0. The main aim of the paper is to investigate the asymptotic dependence of the path functionals: $Y(t) = X(t) - \inf_{0\leq s\leq t}X(s)$,…
Much of mechanistic interpretability has focused on understanding the activation spaces of large neural networks. However, activation space-based approaches reveal little about the underlying circuitry used to compute features. To better…
Semantic image segmentation is an important computer vision task that is difficult because it consists of both recognition and segmentation. The task is often cast as a structured output problem on an exponentially large output-space, which…
For a given L\'{e}vy process $X=(X_t)_{t\in\mathbb{R}_+}$ and for fixed $s\in \mathbb{R}_{+}\cup\{\infty\}$ and $t\in\mathbb{R}_+$ we analyse the {\it future drawdown extremes} that are defined as follows: \begin{eqnarray*} \overline…
The superposition of two independent point processes can be described by multiplication of their probability generating functionals (p.g.fl.s). The inverse operation, which can be viewed as a deconvolution, is defined by dividing the…
As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function…
This paper presents an approach to estimating a hidden process in a continuous-time setting, where the hidden process is a diffusion. The approach is simply to minimize the negative log-likelihood of the hidden path, where the likelihood is…